Problem: Solve for $x$ and $y$ using elimination. ${x-2y = -6}$ ${-x-5y = -22}$
Answer: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $x$ and $-x$ cancel out. $-7y = -28$ $\dfrac{-7y}{{-7}} = \dfrac{-28}{{-7}}$ ${y = 4}$ Now that you know ${y = 4}$ , plug it back into $\thinspace {x-2y = -6}\thinspace$ to find $x$ ${x - 2}{(4)}{= -6}$ $x-8 = -6$ $x-8{+8} = -6{+8}$ ${x = 2}$ You can also plug ${y = 4}$ into $\thinspace {-x-5y = -22}\thinspace$ and get the same answer for $x$ : ${-x - 5}{(4)}{= -22}$ ${x = 2}$